Talks in mathematical physics

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Spring Semester 2019

Date / Time

Speaker

Title

Location

21 February 2019
15:15-16:15

Michele Schiavina
ETH Zurich

Event Details

Talks in Mathematical Physics

Title	Towards holography in the BV-BFV setting
Speaker, Affiliation	Michele Schiavina, ETH Zurich
Date, Time	21 February 2019, 15:15-16:15
Location	HG G 43
Abstract	The BV-BFV formalism, developed by Cattaneo, Mnev and Reshetikhin, who put BV together with BFV following Batalin, Fradkin and Vilkovisky, is a useful framework to handle field theories with symmetries on manifolds with boundaries and corners, which describes gauge invariant quantities while consistently taking into account higher-codimension data. In this language, one can establish a bulk-boundary correspondence in field theory, thus understanding observables, gauge fixing and quantisation of field theories, aiming at an axiomatisation that is compatible with cutting and gluing of stratified manifolds. Several questions arise when looking at the relationship between field theories and their boundary counterparts, such as the problem of Witten descent equations, the correspondence between, e.g., Chern—Simons theory and chiral, conformal field theories and, ultimately, holography. In this talk, after presenting the basics of the (classical) BV-BFV approach to field theories, I will argue how all of the above might be aspects of the same phenomenon, and how the BV-BFV approach might encompass all such aspects in a particularly efficient way. Specifically, I will show how the BV-BFV data of a field theory provides a solution to Witten descent equations, and how this is related to the well know CS-WZW correspondence. This is joint work with P. Mnev and K. Wernli.

Towards holography in the BV-BFV settingread_more

HG G 43

* 7 March 2019
14:15-15:15

Marko Berghoff
HU Berlin

Event Details

Talks in Mathematical Physics

Title	Feynman integrals and graph complexes
Speaker, Affiliation	Marko Berghoff, HU Berlin
Date, Time	7 March 2019, 14:15-15:15
Location	HG G G43
Abstract	Understanding the analytic structure of Feynman integrals is a longstanding open problem in perturbative quantum field theory. Quite recently D. Kreimer and S. Bloch have suggested a new approach to study this problem by methods from geometric group theory, i.e. by using Culler-Vogtmann Outer space and related spaces. The basic idea behind their approach is that the combinatorial and topological data needed to study the analytic properties of Feynman integrals is encoded in the cellular structure of an ''Outer space of Feynman diagrams''. Moreover, its global properties seem to carry information about (new) relations between Feynman integrals. In order to define this space one needs to populate classical Outer space with labelled graphs which model the Feynman diagrams of a given field theory. This gives rise to various moduli spaces of labelled graphs which are pretty interesting in their own right having a rich combinatorial and topological structure. In this talk I will give a brief introduction to this field of study, then define and discuss these moduli spaces of Feynman diagrams and sketch their possible applications in physics and mathematics.

Feynman integrals and graph complexesread_more

HG G G43

19 March 2019
10:00-16:15

Event Details

Talks in Mathematical Physics

Title	Minisymposium Link Homology and TQFTs
Speaker, Affiliation
Date, Time	19 March 2019, 10:00-16:15
Location	Y27 H 26
Abstract	https://www.math.uzh.ch/index.php?id=konferenzdetails0&key1=573

Minisymposium Link Homology and TQFTsread_more

Y27 H 26

21 March 2019
15:15-16:15

Qingtao Chen
NYU Abu Dhabi

Event Details

Talks in Mathematical Physics

Title	Cyclotomic expansion and Volume Conjecture of colored SU(N) invariants with Young Tableau type N^p
Speaker, Affiliation	Qingtao Chen, NYU Abu Dhabi
Date, Time	21 March 2019, 15:15-16:15
Location	HG G 43
Abstract	In this talk, I will first review the original cyclotomic expansion theorem due to Habiro and original Volume Conjecture due to Kashaev-Murakami-Murakami of colored Jones polynomials. Then I will discuss their extension to colored SU(N) invariants with Young Tableau type N, which is a joint work with Kefeng Liu and Shengmao Zhu. Finally I will discuss their extension to colored SU(N) invariants with Young Tableau type N^p, which is a joint work with Giovanni Felder and Huafeng Zhang. If time permits, I will also discuss their extension to superpolynomials.

Cyclotomic expansion and Volume Conjecture of colored SU(N) invariants with Young Tableau type N^pread_more

HG G 43

4 April 2019
15:15-16:15

Erik Panzer
Oxford University

Event Details

Talks in Mathematical Physics

Title	Multiple zeta values as periods of moduli spaces of marked discs in deformation quantization
Speaker, Affiliation	Erik Panzer, Oxford University
Date, Time	4 April 2019, 15:15-16:15
Location	HG G 43
Abstract	Kontsevich's 1997 proof of the formality conjecture provides a universal quantization of every Poisson manifold, by a formal power series whose coefficients are integrals over moduli spaces of marked discs. In joint work with Peter Banks and Brent Pym, we prove that these integrals evaluate to multiple zeta values, which are interesting transcendental numbers known from the KZ associator and as the periods of mixed Tate motives. Our proof is algorithmic and allows for the explicit computation of arbitrary coefficients in the formality morphism, in particular the star product. The essential tools are Francis Brown's theory of polylogarithms on the moduli space of marked genus zero curves, single-valued integration due to Oliver Schnetz, and an induction over the natural fibrations of moduli spaces.

Multiple zeta values as periods of moduli spaces of marked discs in deformation quantizationread_more

HG G 43

18 April 2019
15:15-16:15

Samson Shatashvili
Trinity College, Dublin

Event Details

Talks in Mathematical Physics

Title	On Bethe/Gauge correspondence
Speaker, Affiliation	Samson Shatashvili, Trinity College, Dublin
Date, Time	18 April 2019, 15:15-16:15
Location	HG G 43
Abstract	I review the relationship between supersymmetric gauge theories and quantum integrable systems, often called Bethe/gauge correspondence. From the quantum integrability side this relation includes various spin chains as well as many well-known quantum many body systems like elliptic Calogero-Moser system and generalizations. Key notions appearing in the topic of quantum integrability, such as Baxter equation, Yang-Yang function, Bethe equations, spectral curve, quantum affine algebra - all acquire meaning in this correspondence on the gauge theory side.

On Bethe/Gauge correspondenceread_more

HG G 43

9 May 2019
15:15-16:15

Ajay Ramadoss
Indiana University Bloomington

Event Details

Talks in Mathematical Physics

Title	Dual Hodge decompositions and derived Poisson brackets (joint work with Yuri Berest and Yining Zhang)
Speaker, Affiliation	Ajay Ramadoss, Indiana University Bloomington
Date, Time	9 May 2019, 15:15-16:15
Location	HG G 43
Abstract	We discuss the general properties of Hodge type decompositions of cyclic and Hochschild homology of universal enveloping algebras of (DG) Lie algebras. We give a topological interpretation of such Lie Hodge decompositions in terms of S¹-equivariant homology of the free loop space of a simply connected topological space. Our main result states that the canonical derived Poisson structure on a universal enveloping algebra arising from a cyclic pairing on the Koszul dual coalgebra preserves the Hodge filtration on cyclic homology. It follows that the Chas-Sullivan Lie algebra of a simply connected closed manifold carries a Hodge filtration. It turns out that the Chas-Sullivan Lie algebra is actually graded, i.e. the string topology bracket preserves the Hodge decomposition.

Dual Hodge decompositions and derived Poisson brackets (joint work with Yuri Berest and Yining Zhang)read_more

HG G 43

16 May 2019
15:15-16:15

Tim Weelinck
University of Edinburgh

Event Details

Talks in Mathematical Physics

Title	D-modules on quantum symmetric spaces via factorization homology
Speaker, Affiliation	Tim Weelinck, University of Edinburgh
Date, Time	16 May 2019, 15:15-16:15
Location	HG G 43
Abstract	Factorization homology, as developed by Lurie, Ayala-Francis, Costello-Gwilliam and others provides a mathematical framework that describes the algebraic structures of observables in topological field theories. Concretely, after fixing some algebraic data such as an E_n-algebra (the local observables) one assigns to an n-manifold a functorial invariant (the global observables). In this talk we explain how to extend factorization homology to a context where manifolds are equipped with finite group actions. We then describe a concrete example coming from the theory of quantum groups and quantum symmetric pairs. In particular, we will provide visual intuition why quantum symmetric pairs give rise to two-dimensional Z/2Z-factorization homology. We conclude by discussing some concrete invariants (e.g. the ones mentioned in the title).

D-modules on quantum symmetric spaces via factorization homologyread_more

HG G 43

23 May 2019
15:15-16:15

Andrea Nützi
ETH Zurich, Switzerland

Event Details

Talks in Mathematical Physics

Title	Semiglobal big bang solutions to the Einstein-scalar field system
Speaker, Affiliation	Andrea Nützi, ETH Zurich, Switzerland
Date, Time	23 May 2019, 15:15-16:15
Location	HG G 43
Abstract	We construct a class of semiglobal singular spacetimes for the Einstein equations coupled to a massless scalar field. Consistent with the heuristic analysis of Belinskii, Khalatnikov, Lifshitz for this system, there are no oscillations due to the scalar field. We discuss a formulation of the Einstein equations as the Maurer Cartan equations in a graded Lie algebra; construct formal power series solutions by showing that an obstruction space is zero; and use the formal solutions to then obtain actual solutions to the Einstein equations based on symmetric hyperbolic gauge fixing. An important role is played by a filtration, the MC equations in its associated graded can be solved explicitly. Based on joint work with M. Reiterer and E. Trubowitz.

Semiglobal big bang solutions to the Einstein-scalar field system read_more

HG G 43

* 6 June 2019
15:15-16:15

Ricardo Campos
Université de Montpellier

Event Details

Talks in Mathematical Physics

Title	The homotopy type of associative and commutative algebras
Speaker, Affiliation	Ricardo Campos, Université de Montpellier
Date, Time	6 June 2019, 15:15-16:15
Location	HG F 26.5
Abstract	Given a (dg) commutative algebra, one can ask how much of its homotopy type is contained in its associative part. More precisely one can ask if C and C' are commutative algebras connected by a zig-zag of quasi-isomorphisms of associative algebras, must C and C' be quasi-isomorphic as commutative algebras? Despite its elementary formulation, this question turns out to be surprisingly subtle. In this talk, I will show how one can use operadic deformation theory to give an affirmative answer to this question in characteristic zero. We will also see how the Koszul duality between Lie algebras and commutative algebras allows us to use similar arguments to deduce that Lie algebras are determined by the (associative algebra structure of) their universal envelopping algebras. (Joint with Dan Petersen, Daniel Robert-Nicoud and Felix Wierstra and based on arXiv:1904.03585)

The homotopy type of associative and commutative algebrasread_more

HG F 26.5

3 July 2019
15:15-16:15

Pavel Mnev
University of Notre Dame

Event Details

Talks in Mathematical Physics

Title	Two-dimensional Yang-Mills theory on surfaces with corners in Batalin-Vilkovisky formalism
Speaker, Affiliation	Pavel Mnev, University of Notre Dame
Date, Time	3 July 2019, 15:15-16:15
Location	Y27 H 12
Abstract	We recover the Migdal-Witten nonperturbative partition function of Yang-Mills theory on surfaces, given in terms of representation theory of the structure group, via perturbative path integral quantization. The strategy is to embed the theory in a version of Batalin-Vilkovisky formalism compatible with cutting with corners. We cut the surface into pieces admitting a gauge-fixing where explicit computation of all Feynman diagrams is possible (e.g. the axial gauge), and then assemble the answers for pieces together via a gluing formula. Our answers for Yang-Mills with corners fit with Baez-Dolan-Lurie paradigm of extended TQFTs (decorated with areas), assigning algebras to points, bimodules to intervals and morphisms of bimodules to disks. This is a report on a joint work with Riccardo Iraso arXiv:1806.04172.

Two-dimensional Yang-Mills theory on surfaces with corners in Batalin-Vilkovisky formalismread_more

Y27 H 12

4 July 2019
15:15-16:15

Pavel Mnev
University of Notre Dame

Event Details

Talks in Mathematical Physics

Title	Two-dimensional BF theory as a conformal field theory
Speaker, Affiliation	Pavel Mnev, University of Notre Dame
Date, Time	4 July 2019, 15:15-16:15
Location	HG G 43
Abstract	We study topological BF theory on the complex plane in Lorenz gauge. In the abelian case, we find that the gauge-fixed theory is a B-twisted N=(2,2) superconformal theory - Witten's B-model with a parity-reversed target. The BV algebra structure on 0-observables is constructed explicitly using operator product expansions with the superpartner of the stress-energy tensor. In the non-abelian case, the theory becomes a logarithmic CFT with correlators given by convergent integrals (e.g., 4-point functions are expressed in terms of dilogarithms). We find vertex operators in the non-abelian theory, receiving a quantum correction to conformal dimension. This is a report on a joint work with Andrey Losev and Donald Youmans, arXiv:1712.01186, arXiv:1902.02738.

Two-dimensional BF theory as a conformal field theoryread_more

HG G 43

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